Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 788 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.₹368 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹46 (b) ₹368 (c) ₹322 (d) ₹184
2. 2.If 7 pens cost ₹105, how much do 5 pens cost? (a) ₹525 (b) ₹103 (c) ₹90 (d) ₹75
3. 3.If 4 pens cost ₹24, how much do 6 pens cost? (a) ₹26 (b) ₹144 (c) ₹42 (d) ₹36
4. 4.If 8 kites cost ₹96, how much do 2 kites cost? (a) ₹192 (b) ₹24 (c) ₹90 (d) ₹36
5. 5.₹240 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹120 (b) ₹24 (c) ₹240 (d) ₹216
6. 6.If 7 pens cost ₹49, how much do 8 pens cost? (a) ₹50 (b) ₹56 (c) ₹63 (d) ₹392
7. 7.If 8 pens cost ₹88, how much do 9 pens cost? (a) ₹89 (b) ₹792 (c) ₹110 (d) ₹99
8. 8.₹275 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹25 (b) ₹200 (c) ₹100 (d) ₹175
9. 9.If 9 notebooks cost ₹189, how much do 7 notebooks cost? (a) ₹168 (b) ₹1323 (c) ₹187 (d) ₹147
10. 10.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹246 (b) ₹287 (c) ₹41 (d) ₹205
11. 11.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 54 days (b) 19 days (c) 5 days (d) 55 days
12. 12.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹114 (d) ₹133
13. 13.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 9 days (d) 3 days
14. 14.₹539 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹392 (b) ₹196 (c) ₹49 (d) ₹343
15. 15.If 8 pens cost ₹72, how much do 10 pens cost? (a) ₹99 (b) ₹720 (c) ₹90 (d) ₹74
16. 16.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 13 days (d) 5 days
17. 17.₹75 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹25 (b) ₹51 (c) ₹50 (d) ₹75
18. 18.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹250 (b) ₹400 (c) ₹325 (d) ₹50
19. 19.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 12 days (d) 4 days
20. 20.If 4 pens cost ₹24, how much do 7 pens cost? (a) ₹48 (b) ₹27 (c) ₹168 (d) ₹42
21. 21.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 8 days (d) 2 days
22. 22.If 3 mangoes cost ₹66, how much do 5 mangoes cost? (a) ₹132 (b) ₹68 (c) ₹330 (d) ₹110
23. 23.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹11 (b) ₹89 (c) ₹88 (d) ₹99
24. 24.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 21 days (d) 17 days
25. 25.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹45 (c) ₹15 (d) ₹30
26. 26.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹266 (b) ₹38 (c) ₹304 (d) ₹152
27. 27.If 9 notebooks cost ₹72, how much do 4 notebooks cost? (a) ₹67 (b) ₹40 (c) ₹288 (d) ₹32
28. 28.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹33 (b) ₹11 (c) ₹22 (d) ₹23
29. 29.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹91 (b) ₹26 (c) ₹104 (d) ₹78
30. 30.₹330 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹165 (b) ₹99 (c) ₹33 (d) ₹231
31. 31.If 3 kites cost ₹12, how much do 8 kites cost? (a) ₹36 (b) ₹17 (c) ₹32 (d) ₹96
32. 32.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 9 days (d) 12 days
33. 33.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹165 (b) ₹198 (c) ₹33 (d) ₹231
34. 34.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 12 days (d) 1 day
35. 35.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 11 days (d) 26 days
36. 36.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹136 (b) ₹17 (c) ₹85 (d) ₹153
37. 37.₹243 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹216 (b) ₹243 (c) ₹217 (d) ₹27
38. 38.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹16 (b) ₹20 (c) ₹25 (d) ₹60
39. 39.If 5 mangoes cost ₹65, how much do 10 mangoes cost? (a) ₹130 (b) ₹143 (c) ₹70 (d) ₹650
40. 40.₹102 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹85 (b) ₹102 (c) ₹17 (d) ₹51

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